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5pt'><span
lang=3DEN-US>f =3Dx^2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>a0 =3D2/3*pi^2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>an</span></span><span lang=3DEN-US>
=3D2*(n^2*pi^2*sin(pi*n)-2*sin(pi*n)+2*pi*n*<span class=3DSpellE>cos</span>=
(pi*n))/n^3/pi</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>bn</span></span></spa=
n><span
lang=3DEN-US> =3D0</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>这里，我们得到ߚ=
2;傅立叶系数的公式，&=
#21482;要代入具体的</span><span
lang=3DEN-US>n</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>就可以得&#=
21040;结果了。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>考虑到不同函数=
做傅立叶展开时，公=
4335;是一致的，因此，ৎ=
5;们可以编制一个函数&=
#65292;专门用来计算函数=
340;傅立叶系数，改函数=
;如下：</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>function</span></span><span lang=3DEN-US>
[a0,ak,bk]=3D<span class=3DSpellE>myfly</span>(f)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>syms</span></span></s=
pan><span
lang=3DEN-US> k x</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>a0=3D<span class=3DSpellE><span class=3DGramE>int</span></span=
><span
class=3DGramE>(</span><span class=3DSpellE>f,x,-pi,pi</span>)/pi;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>ak</span></span></spa=
n><span
class=3DGramE><span lang=3DEN-US>=3D</span></span><span class=3DSpellE><span
lang=3DEN-US>int</span></span><span lang=3DEN-US>(f*<span class=3DSpellE>co=
s</span>(k*x),x,-<span
class=3DSpellE>pi,pi</span>)/pi;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>bk</span></span></spa=
n><span
class=3DGramE><span lang=3DEN-US>=3D</span></span><span class=3DSpellE><span
lang=3DEN-US>int</span></span><span lang=3DEN-US>(f*sin(k*x),x,-<span class=
=3DSpellE>pi,pi</span>)/pi;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><span style=3D'=
font-family:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>注意，该文件一ऩ=
0;要以</span><span
class=3DSpellE><span lang=3DEN-US>mfly.m</span></span><span style=3D'font-f=
amily:
SimSun;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times=
New Roman"'>为文件名。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>这样得到的是公=
式，如果要计算出具=
0307;的数值，则可以用ߍ=
9;面的方法实现：</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>现将</span><span class=3DSpellE><span lang=
=3DEN-US>ak</span></span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>，</span><span class=3DSpellE><span lang=3DEN-US>b=
k</span></span><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>的计算公式分别=
编制成独立的函数，=
4182;以相应的文件名命ࡧ=
7;。这里先编制两个</span><s=
pan
lang=3DEN-US>m</span><span style=3D'font-family:SimSun;mso-ascii-font-famil=
y:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>文件，其&#=
20869;容分别为：</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>%<span class=3DSpellE>fourieran.m</span></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>function</span></span><span lang=3DEN-US> =
an=3D<span
class=3DSpellE>fourieran</span>(<span class=3DSpellE>f,n</span>)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>syms</span></span></s=
pan><span
lang=3DEN-US> x</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>an=3D</span></span><span class=3DSpellE><s=
pan
lang=3DEN-US>int</span></span><span lang=3DEN-US>(f*<span class=3DSpellE>co=
s</span>(n*x),x,-<span
class=3DSpellE>pi,pi</span>)/pi;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>%<span class=3DSpellE>fourierbn.m</span></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>function</span></span><span lang=3DEN-US> =
<span
class=3DSpellE>bn</span>=3D<span class=3DSpellE>fourierbn</span>(<span clas=
s=3DSpellE>f,n</span>)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>syms</span></span></s=
pan><span
lang=3DEN-US> x</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>bn</span></span></spa=
n><span
class=3DGramE><span lang=3DEN-US>=3D</span></span><span class=3DSpellE><span
lang=3DEN-US>int</span></span><span lang=3DEN-US>(f*sin(n*x),x,-<span class=
=3DSpellE>pi,pi</span>)/pi;</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>接着，再编写程=
序如下：</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>clear</span></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DSpellE><span class=3DGramE><span lang=3DEN-US>syms</span></span></s=
pan><span
lang=3DEN-US> x n</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>f=3Dx^2</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>a0=3D<span class=3DSpellE><span class=3DGramE>fourieran</span>=
</span><span
class=3DGramE>(</span>f,0);</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>a=3D<span class=3DGramE>zeros(</span>1,10)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>b=3D<span class=3DGramE>zeros(</span>1,10)</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>for</span></span><span lang=3DEN-US> n=3D1=
:10</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'> </span><sp=
an
class=3DGramE>a(</span>n)=3D<span class=3DSpellE>eval</span>(<span class=3D=
SpellE>fourieran</span>(<span
class=3DSpellE>f,n</span>));</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>end</span></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>for</span></span><span lang=3DEN-US> n=3D1=
:10</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US><span style=3D'mso-spacerun:yes'> </span><sp=
an
class=3DGramE>b(</span>n)=3D<span class=3DSpellE>eval</span>(<span class=3D=
SpellE>fourierbn</span>(<span
class=3DSpellE>f,n</span>));</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
class=3DGramE><span lang=3DEN-US>end</span></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US>a,b</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
style=3D'font-family:SimSun;mso-ascii-font-family:"Times New Roman";mso-han=
si-font-family:
"Times New Roman"'>即可完成前</span><span
lang=3DEN-US>21</span><span style=3D'font-family:SimSun;mso-ascii-font-fami=
ly:"Times New Roman";
mso-hansi-font-family:"Times New Roman"'>个傅立叶&#=
31995;数的计算。</span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left;text-indent:21.7=
5pt'><span
lang=3DEN-US><o:p> </o:p></span></p>
<p class=3DMsoNormal align=3Dleft style=3D'text-align:left'><b style=3D'mso=
-bidi-font-weight:
normal'><span style=3D'font-family:SimSun;mso-ascii-font-family:"Times New =
Roman";
mso-hansi-font-family:"Times New Roman"'>三、实验&#=
20869;容</span><span
lang=3DEN-US><o:p></o:p></span></b></p>
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